Merge branch 'master' into client-routesv2

app/models/concerns/user.rb

@@ -8,6 +8,11 @@ module User
     has_many :exercises, as: :user
     has_many :file_types, as: :user
     has_many :submissions, as: :user
+    has_many :user_proxy_exercise_exercises, as: :user
+    has_many :user_exercise_interventions, as: :user
+    has_many :interventions, through: :user_exercise_interventions
+    accepts_nested_attributes_for :user_proxy_exercise_exercises
+
 
     scope :with_submissions, -> { where('id IN (SELECT user_id FROM submissions)') }
   end
@@ -21,6 +26,6 @@ module User
   end
 
   def to_s
-    name
+    displayname
   end
 end

app/models/exercise.rb

@@ -12,6 +12,15 @@ class Exercise < ActiveRecord::Base
   belongs_to :execution_environment
   has_many :submissions
 
+  has_and_belongs_to_many :proxy_exercises
+  has_many :user_proxy_exercise_exercises
+  has_and_belongs_to_many :exercise_collections
+  has_many :user_exercise_interventions
+  has_many :interventions, through: :user_exercise_interventions
+  has_many :exercise_tags
+  has_many :tags, through: :exercise_tags
+  accepts_nested_attributes_for :exercise_tags
+
   has_many :external_users, source: :user, source_type: ExternalUser, through: :submissions
   has_many :internal_users, source: :user, source_type: InternalUser, through: :submissions
   alias_method :users, :external_users
@@ -48,17 +57,21 @@ class Exercise < ActiveRecord::Base
     return user_count == 0 ? 0 : submissions.count() / user_count.to_f()
   end
 
+  def time_maximum_score(user)
+    submissions.where(user: user).where("cause IN ('submit','assess')").where("score IS NOT NULL").order("score DESC, created_at ASC").first.created_at rescue Time.zone.at(0)
+  end
+
   def user_working_time_query
     """
       SELECT user_id,
              sum(working_time_new) AS working_time
       FROM
         (SELECT user_id,
-                CASE WHEN working_time >= '0:30:00' THEN '0' ELSE working_time END AS working_time_new
+                CASE WHEN working_time >= '0:05:00' THEN '0' ELSE working_time END AS working_time_new
          FROM
             (SELECT user_id,
                     id,
-                    (created_at - lag(created_at) over (PARTITION BY user_id
+                    (created_at - lag(created_at) over (PARTITION BY user_id, exercise_id
                                                         ORDER BY created_at)) AS working_time
             FROM submissions
             WHERE exercise_id=#{id}) AS foo) AS bar
@@ -66,6 +79,123 @@ class Exercise < ActiveRecord::Base
     """
   end
 
+  def get_quantiles(quantiles)
+    quantiles_str = "[" + quantiles.join(",") + "]"
+    result = self.class.connection.execute("""
+            WITH working_time AS
+      (
+               SELECT   user_id,
+                        id,
+                        exercise_id,
+                        Max(score)                                                                                  AS max_score,
+                        (created_at - Lag(created_at) OVER (partition BY user_id, exercise_id ORDER BY created_at)) AS working_time
+               FROM     submissions
+               WHERE    exercise_id = #{id}
+               AND      user_type = 'ExternalUser'
+               GROUP BY user_id,
+                        id,
+                        exercise_id), max_points AS
+      (
+               SELECT   context_id  AS ex_id,
+                        Sum(weight) AS max_points
+               FROM     files
+               WHERE    context_type = 'Exercise'
+               AND      context_id = #{id}
+               AND      role = 'teacher_defined_test'
+               GROUP BY context_id),
+      -- filter for rows containing max points
+      time_max_score AS
+      (
+             SELECT *
+             FROM   working_time W1,
+                    max_points MS
+             WHERE  w1.exercise_id = ex_id
+             AND    w1.max_score = ms.max_points),
+      -- find row containing the first time max points
+      first_time_max_score AS
+      (
+             SELECT id,
+                    user_id,
+                    exercise_id,
+                    max_score,
+                    working_time,
+                    rn
+             FROM   (
+                             SELECT   id,
+                                      user_id,
+                                      exercise_id,
+                                      max_score,
+                                      working_time,
+                                      Row_number() OVER(partition BY user_id, exercise_id ORDER BY id ASC) AS rn
+                             FROM     time_max_score) T
+             WHERE  rn = 1), times_until_max_points AS
+      (
+             SELECT w.id,
+                    w.user_id,
+                    w.exercise_id,
+                    w.max_score,
+                    w.working_time,
+                    m.id AS reachedmax_at
+             FROM   working_time W,
+                    first_time_max_score M
+             WHERE  w.user_id = m.user_id
+             AND    w.exercise_id = m.exercise_id
+             AND    w.id <= m.id),
+      -- if user never makes it to max points, take all times
+      all_working_times_until_max AS (
+      (
+             SELECT id,
+                    user_id,
+                    exercise_id,
+                    max_score,
+                    working_time
+             FROM   times_until_max_points)
+      UNION ALL
+                (
+                       SELECT id,
+                              user_id,
+                              exercise_id,
+                              max_score,
+                              working_time
+                       FROM   working_time W1
+                       WHERE  NOT EXISTS
+                              (
+                                     SELECT 1
+                                     FROM   first_time_max_score F
+                                     WHERE  f.user_id = w1.user_id
+                                     AND    f.exercise_id = w1.exercise_id))), filtered_times_until_max AS
+      (
+             SELECT user_id,
+                    exercise_id,
+                    max_score,
+                    CASE
+                           WHEN working_time >= '0:05:00' THEN '0'
+                           ELSE working_time
+                    END AS working_time_new
+             FROM   all_working_times_until_max ), result AS
+      (
+               SELECT   e.external_id AS external_user_id,
+                        f.user_id,
+                        exercise_id,
+                        Max(max_score)        AS max_score,
+                        Sum(working_time_new) AS working_time
+               FROM     filtered_times_until_max f,
+                        external_users e
+               WHERE    f.user_id = e.id
+               GROUP BY e.external_id,
+                        f.user_id,
+                        exercise_id )
+      SELECT   unnest(percentile_cont(array#{quantiles_str}) within GROUP (ORDER BY working_time))
+      FROM     result
+    """)
+    if result.count > 0
+      quantiles.each_with_index.map{|q,i| Time.parse(result[i]["unnest"]).seconds_since_midnight}
+    else
+      quantiles.map{|q| 0}
+    end
+
+  end
+
   def retrieve_working_time_statistics
     @working_time_statistics = {}
     self.class.connection.execute(user_working_time_query).each do |tuple|
@@ -88,23 +218,64 @@ class Exercise < ActiveRecord::Base
     @working_time_statistics[user_id]["working_time"]
   end
 
-  def average_working_time_for_only(user_id)
-    self.class.connection.execute("""
-      SELECT sum(working_time_new) AS working_time
-      FROM
-        (SELECT CASE WHEN working_time >= '0:30:00' THEN '0' ELSE working_time END AS working_time_new
-         FROM
-            (SELECT id,
-                    (created_at - lag(created_at) over (PARTITION BY user_id
-                                                        ORDER BY created_at)) AS working_time
-            FROM submissions
-            WHERE exercise_id=#{id} and user_id=#{user_id}) AS foo) AS bar
-    """).first["working_time"]
+  def accumulated_working_time_for_only(user)
+    user_type = user.external_user? ? "ExternalUser" : "InternalUser"
+    Time.parse(self.class.connection.execute("""
+        WITH WORKING_TIME AS
+        (SELECT user_id,
+                           id,
+                           exercise_id,
+                           max(score) AS max_score,
+                           (created_at - lag(created_at) OVER (PARTITION BY user_id, exercise_id
+                                                               ORDER BY created_at)) AS working_time
+                   FROM submissions
+                   WHERE exercise_id = #{id} AND user_id = #{user.id} AND user_type = '#{user_type}'
+                   GROUP BY user_id, id, exercise_id),
+        MAX_POINTS AS
+        (SELECT context_id AS ex_id, sum(weight) AS max_points FROM files WHERE context_type = 'Exercise' AND context_id = #{id} AND role = 'teacher_defined_test' GROUP BY context_id),
+
+        -- filter for rows containing max points
+        TIME_MAX_SCORE AS
+        (SELECT *
+        FROM WORKING_TIME W1, MAX_POINTS MS
+        WHERE W1.exercise_id = ex_id AND W1.max_score = MS.max_points),
+
+        -- find row containing the first time max points
+        FIRST_TIME_MAX_SCORE AS
+        ( SELECT id,USER_id,exercise_id,max_score,working_time, rn
+          FROM (
+            SELECT id,USER_id,exercise_id,max_score,working_time,
+                ROW_NUMBER() OVER(PARTITION BY user_id, exercise_id ORDER BY id ASC) AS rn
+            FROM TIME_MAX_SCORE) T
+         WHERE rn = 1),
+
+        TIMES_UNTIL_MAX_POINTS AS (
+            SELECT W.id, W.user_id, W.exercise_id, W.max_score, W.working_time, M.id AS reachedmax_at
+            FROM WORKING_TIME W, FIRST_TIME_MAX_SCORE M
+            WHERE W.user_id = M.user_id AND W.exercise_id = M.exercise_id AND W.id <= M.id),
+
+        -- if user never makes it to max points, take all times
+        ALL_WORKING_TIMES_UNTIL_MAX AS
+        ((SELECT id, user_id, exercise_id, max_score, working_time FROM TIMES_UNTIL_MAX_POINTS)
+        UNION ALL
+        (SELECT id, user_id, exercise_id, max_score, working_time FROM WORKING_TIME W1
+         WHERE NOT EXISTS (SELECT 1 FROM FIRST_TIME_MAX_SCORE F WHERE F.user_id = W1.user_id AND F.exercise_id = W1.exercise_id))),
+
+        FILTERED_TIMES_UNTIL_MAX AS
+        (
+        SELECT user_id,exercise_id, max_score, CASE WHEN working_time >= '0:05:00' THEN '0' ELSE working_time END AS working_time_new
+        FROM ALL_WORKING_TIMES_UNTIL_MAX
+        )
+            SELECT e.external_id AS external_user_id, f.user_id, exercise_id, MAX(max_score) AS max_score, sum(working_time_new) AS working_time
+            FROM FILTERED_TIMES_UNTIL_MAX f, EXTERNAL_USERS e
+            WHERE f.user_id = e.id GROUP BY e.external_id, f.user_id, exercise_id
+    """).first["working_time"]).seconds_since_midnight rescue 0
   end
 
   def duplicate(attributes = {})
     exercise = dup
     exercise.attributes = attributes
+    exercise_tags.each  { |et| exercise.exercise_tags << et.dup }
     files.each { |file| exercise.files << file.dup }
     exercise
   end
@@ -162,8 +333,16 @@ class Exercise < ActiveRecord::Base
   end
   private :generate_token
 
-  def maximum_score
-    files.teacher_defined_tests.sum(:weight)
+  def maximum_score(user = nil)
+    if user
+      submissions.where(user: user).where("cause IN ('submit','assess')").where("score IS NOT NULL").order("score DESC").first.score || 0 rescue 0
+    else
+      files.teacher_defined_tests.sum(:weight)
+    end
+  end
+
+  def has_user_solved(user)
+    return maximum_score(user).to_i == maximum_score.to_i
   end
 
   def set_default_values

app/models/exercise_collection.rb

@@ -0,0 +1,5 @@
+class ExerciseCollection < ActiveRecord::Base
+
+  has_and_belongs_to_many :exercises
+
+end

app/models/exercise_tag.rb

@@ -0,0 +1,13 @@
+class ExerciseTag < ActiveRecord::Base
+
+  belongs_to :tag
+  belongs_to :exercise
+
+  before_save :destroy_if_empty_exercise_or_tag
+
+  private
+  def destroy_if_empty_exercise_or_tag
+     destroy if exercise_id.blank? || tag_id.blank?
+  end
+
+end

app/models/external_user.rb

@@ -5,8 +5,8 @@ class ExternalUser < ActiveRecord::Base
   validates :external_id, presence: true
 
   def displayname
-    result = name
-    if(consumer.name == 'openHPI')
+    result =  "User " + id.to_s
+    if(!consumer.nil? && consumer.name == 'openHPI')
       result = Rails.cache.fetch("#{cache_key}/displayname", expires_in: 12.hours) do
          Xikolo::UserClient.get(external_id.to_s)[:display_name]
       end

app/models/intervention.rb

@@ -0,0 +1,16 @@
+class Intervention < ActiveRecord::Base
+
+  has_many :user_exercise_interventions
+  has_many :users, through: :user_exercise_interventions, source_type: "ExternalUser"
+
+  def to_s
+    name
+  end
+
+  def self.createDefaultInterventions
+    %w(BreakIntervention QuestionIntervention).each do |name|
+      Intervention.find_or_create_by(name: name)
+    end
+  end
+
+end

app/models/proxy_exercise.rb

@@ -0,0 +1,258 @@
+class ProxyExercise < ActiveRecord::Base
+
+    after_initialize :generate_token
+    after_initialize :set_reason
+
+    has_and_belongs_to_many :exercises
+    has_many :user_proxy_exercise_exercises
+
+    def count_files
+        exercises.count
+    end
+
+    def set_reason
+      @reason = {}
+    end
+
+    def generate_token
+      self.token ||= SecureRandom.hex(4)
+    end
+    private :generate_token
+
+    def duplicate(attributes = {})
+      proxy_exercise = dup
+      proxy_exercise.attributes = attributes
+      proxy_exercise
+    end
+
+    def to_s
+      title
+    end
+
+    def get_matching_exercise(user)
+      assigned_user_proxy_exercise = user_proxy_exercise_exercises.where(user: user).first
+      recommended_exercise =
+        if (assigned_user_proxy_exercise)
+          Rails.logger.debug("retrieved assigned exercise for user #{user.id}: Exercise #{assigned_user_proxy_exercise.exercise}" )
+          assigned_user_proxy_exercise.exercise
+        else
+          matching_exercise =
+            if (token.eql? "47f4c736")
+              Rails.logger.debug("Proxy exercise with token 47f4c736, split user in groups..")
+              group = UserGroupSeparator.getGroupWeek2Testing(user)
+              Rails.logger.debug("user assigned to group #{group}")
+              case group
+                when :group_a
+                  exercises.where(id: 348).first
+                when :group_b
+                  exercises.where(id: 349).first
+                when :group_c
+                  exercises.where(id: 350).first
+                when :group_d
+                  exercises.where(id: 351).first
+              end
+            else
+              Rails.logger.debug("find new matching exercise for user #{user.id}" )
+              begin
+                find_matching_exercise(user)
+              rescue #fallback
+                Rails.logger.error("finding matching exercise failed. Fall back to random exercise! Error: #{$!}" )
+                @reason[:reason] = "fallback because of error"
+                @reason[:error] = "#{$!}"
+                exercises.shuffle.first
+              end
+            end
+          user.user_proxy_exercise_exercises << UserProxyExerciseExercise.create(user: user, exercise: matching_exercise, proxy_exercise: self, reason: @reason.to_json)
+          matching_exercise
+
+
+        end
+      recommended_exercise
+    end
+
+    def find_matching_exercise(user)
+      user_group = UserGroupSeparator.getProxyExerciseGroup(user)
+      case user_group
+        when :dummy_assigment
+          rec_ex = select_easiest_exercise(exercises)
+          @reason[:reason] = "dummy group"
+          Rails.logger.debug("assigned user to dummy group, and gave him exercise: #{rec_ex.title}")
+          rec_ex
+        when :random_assigment
+          @reason[:reason] = "random group"
+          ex = exercises.where("expected_difficulty > 1").shuffle.first
+          Rails.logger.debug("assigned user to random group, and gave him exercise: #{ex.title}")
+          ex
+        when :recommended_assignment
+          exercises_user_has_accessed = user.submissions.where("cause IN ('submit','assess')").map{|s| s.exercise}.uniq.compact
+          tags_user_has_seen = exercises_user_has_accessed.map{|ex| ex.tags}.uniq.flatten
+          Rails.logger.debug("exercises_user_has_accessed #{exercises_user_has_accessed.map{|e|e.id}.join(",")}")
+
+          # find exercises
+          potential_recommended_exercises = []
+          exercises.where("expected_difficulty > 1").each do |ex|
+            ## find exercises which have only tags the user has already seen
+            if (ex.tags - tags_user_has_seen).empty?
+              potential_recommended_exercises << ex
+            end
+          end
+          Rails.logger.debug("potential_recommended_exercises: #{potential_recommended_exercises.map{|e|e.id}}")
+          # if all exercises contain tags which the user has never seen, recommend easiest exercise
+          if potential_recommended_exercises.empty?
+            Rails.logger.debug("matched easiest exercise in pool")
+            @reason[:reason] = "easiest exercise in pool. empty potential exercises"
+            select_easiest_exercise(exercises)
+          else
+            recommended_exercise = select_best_matching_exercise(user, exercises_user_has_accessed, potential_recommended_exercises)
+            recommended_exercise
+          end
+      end
+
+    end
+    private :find_matching_exercise
+
+    def select_best_matching_exercise(user, exercises_user_has_accessed, potential_recommended_exercises)
+      topic_knowledge_user_and_max = get_user_knowledge_and_max_knowledge(user, exercises_user_has_accessed)
+      Rails.logger.debug("topic_knowledge_user_and_max: #{topic_knowledge_user_and_max}")
+      Rails.logger.debug("potential_recommended_exercises: #{potential_recommended_exercises.size}: #{potential_recommended_exercises.map{|p| p.id}}")
+      topic_knowledge_user = topic_knowledge_user_and_max[:user_topic_knowledge]
+      topic_knowledge_max = topic_knowledge_user_and_max[:max_topic_knowledge]
+      current_users_knowledge_lack = {}
+      topic_knowledge_max.keys.each do |tag|
+        current_users_knowledge_lack[tag] = topic_knowledge_user[tag] /  topic_knowledge_max[tag]
+      end
+
+      relative_knowledge_improvement = {}
+      potential_recommended_exercises.each do |potex|
+        tags =  potex.tags
+        relative_knowledge_improvement[potex] = 0.0
+        Rails.logger.debug("review potential exercise #{potex.id}")
+        tags.each do |tag|
+          tag_ratio = potex.exercise_tags.where(tag: tag).first.factor.to_f / potex.exercise_tags.inject(0){|sum, et| sum += et.factor }.to_f
+          max_topic_knowledge_ratio = potex.expected_difficulty * tag_ratio
+          old_relative_loss_tag = topic_knowledge_user[tag] / topic_knowledge_max[tag]
+          new_relative_loss_tag = topic_knowledge_user[tag] / (topic_knowledge_max[tag] + max_topic_knowledge_ratio)
+          Rails.logger.debug("tag #{tag} old_relative_loss_tag #{old_relative_loss_tag}, new_relative_loss_tag #{new_relative_loss_tag}, tag_ratio #{tag_ratio}")
+          relative_knowledge_improvement[potex] += old_relative_loss_tag - new_relative_loss_tag
+        end
+      end
+      highest_difficulty_user_has_accessed =  exercises_user_has_accessed.map{|e| e.expected_difficulty}.sort.last || 0
+      best_matching_exercise = find_best_exercise(relative_knowledge_improvement, highest_difficulty_user_has_accessed)
+      @reason[:reason] = "best matching exercise"
+      @reason[:highest_difficulty_user_has_accessed] = highest_difficulty_user_has_accessed
+      @reason[:current_users_knowledge_lack] = current_users_knowledge_lack
+      @reason[:relative_knowledge_improvement] = relative_knowledge_improvement
+
+      Rails.logger.debug("current users knowledge loss: " + current_users_knowledge_lack.map{|k,v| "#{k} => #{v}"}.to_s)
+      Rails.logger.debug("relative improvements #{relative_knowledge_improvement.map{|k,v| k.id.to_s + ':' + v.to_s}}")
+      best_matching_exercise
+    end
+    private :select_best_matching_exercise
+
+    def find_best_exercise(relative_knowledge_improvement, highest_difficulty_user_has_accessed)
+      Rails.logger.debug("select most appropiate exercise for user. his highest difficulty was #{highest_difficulty_user_has_accessed}")
+      sorted_exercises = relative_knowledge_improvement.sort_by{|k,v| v}.reverse
+
+      sorted_exercises.each do |ex,diff|
+        Rails.logger.debug("review exercise #{ex.id} diff: #{ex.expected_difficulty}")
+        if (ex.expected_difficulty - highest_difficulty_user_has_accessed) <= 1
+          Rails.logger.debug("matched exercise #{ex.id}")
+          return ex
+        else
+          Rails.logger.debug("exercise #{ex.id} is too difficult")
+        end
+      end
+      easiest_exercise = sorted_exercises.min_by{|k,v| v}.first
+      Rails.logger.debug("no match, select easiest exercise as fallback #{easiest_exercise.id}")
+      easiest_exercise
+    end
+    private :find_best_exercise
+
+    # [score][quantile]
+    def scoring_matrix
+      [
+          [0  ,0  ,0  ,0  ,0  ],
+          [0.2,0.2,0.2,0.2,0.1],
+          [0.5,0.5,0.4,0.4,0.3],
+          [0.6,0.6,0.5,0.5,0.4],
+          [1  ,1  ,0.9,0.8,0.7],
+      ]
+    end
+
+    def scoring_matrix_quantiles
+      [0.2,0.4,0.6,0.8]
+    end
+    private :scoring_matrix_quantiles
+
+    def score(user, ex)
+      max_score = ex.maximum_score.to_f
+      if max_score <= 0
+        Rails.logger.debug("scoring user #{user.id} for exercise #{ex.id}:  score: 0" )
+        return 0.0
+      end
+      points_ratio = ex.maximum_score(user) / max_score
+      if points_ratio == 0.0
+        Rails.logger.debug("scoring user #{user.id} for exercise #{ex.id}: points_ratio=#{points_ratio} score: 0" )
+        return 0.0
+      end
+      points_ratio_index = ((scoring_matrix.size - 1)  * points_ratio).to_i
+      working_time_user = ex.accumulated_working_time_for_only(user)
+      quantiles_working_time = ex.get_quantiles(scoring_matrix_quantiles)
+      quantile_index = quantiles_working_time.size
+      quantiles_working_time.each_with_index do |quantile_time, i|
+        if working_time_user <= quantile_time
+          quantile_index = i
+          break
+        end
+      end
+      Rails.logger.debug(
+          "scoring user #{user.id} exercise #{ex.id}: worktime #{working_time_user}, points: #{points_ratio}" \
+          "(index #{points_ratio_index}) quantiles #{quantiles_working_time} placed into quantile index #{quantile_index} " \
+          "score: #{scoring_matrix[points_ratio_index][quantile_index]}")
+      scoring_matrix[points_ratio_index][quantile_index]
+    end
+    private :score
+
+    def get_user_knowledge_and_max_knowledge(user, exercises)
+      # initialize knowledge for each tag with 0
+      all_used_tags_with_count = {}
+      exercises.each do |ex|
+        ex.tags.each do |t|
+          all_used_tags_with_count[t] ||= 0
+          all_used_tags_with_count[t] += 1
+        end
+      end
+      tags_counter = all_used_tags_with_count.keys.map{|tag| [tag,0]}.to_h
+      topic_knowledge_loss_user = all_used_tags_with_count.keys.map{|t| [t, 0]}.to_h
+      topic_knowledge_max = all_used_tags_with_count.keys.map{|t| [t, 0]}.to_h
+      exercises_sorted = exercises.sort_by { |ex| ex.time_maximum_score(user)}
+      exercises_sorted.each do |ex|
+        Rails.logger.debug("exercise: #{ex.id}: #{ex}")
+        user_score_factor = score(user, ex)
+        ex.tags.each do |t|
+          tags_counter[t] += 1
+          tag_diminishing_return_factor = tag_diminishing_return_function(tags_counter[t], all_used_tags_with_count[t])
+          tag_ratio = ex.exercise_tags.where(tag: t).first.factor.to_f / ex.exercise_tags.inject(0){|sum, et| sum += et.factor }.to_f
+          Rails.logger.debug("tag: #{t}, factor: #{ex.exercise_tags.where(tag: t).first.factor}, sumall: #{ex.exercise_tags.inject(0){|sum, et| sum += et.factor }}")
+          Rails.logger.debug("tag #{t}, count #{tags_counter[t]}, max: #{all_used_tags_with_count[t]}, factor: #{tag_diminishing_return_factor}")
+          Rails.logger.debug("tag_ratio #{tag_ratio}")
+          topic_knowledge_ratio = ex.expected_difficulty * tag_ratio
+          Rails.logger.debug("topic_knowledge_ratio #{topic_knowledge_ratio}")
+          topic_knowledge_loss_user[t] += (1 - user_score_factor) * topic_knowledge_ratio * tag_diminishing_return_factor
+          topic_knowledge_max[t] += topic_knowledge_ratio * tag_diminishing_return_factor
+        end
+      end
+      {user_topic_knowledge: topic_knowledge_loss_user, max_topic_knowledge: topic_knowledge_max}
+    end
+    private :get_user_knowledge_and_max_knowledge
+
+    def tag_diminishing_return_function(count_tag, total_count_tag)
+      total_count_tag += 1 # bonus exercise comes on top
+      return 1/(1+(Math::E**(-3/(0.5*total_count_tag)*(count_tag-0.5*total_count_tag))))
+    end
+
+    def select_easiest_exercise(exercises)
+      exercises.order(:expected_difficulty).first
+    end
+
+end

app/models/search.rb

@@ -0,0 +1,4 @@
+class Search < ActiveRecord::Base
+  belongs_to :user, polymorphic: true
+  belongs_to :exercise
+end

app/models/tag.rb

@@ -0,0 +1,22 @@
+class Tag < ActiveRecord::Base
+
+  has_many :exercise_tags
+  has_many :exercises, through: :exercise_tags
+
+  validates_uniqueness_of :name
+
+  def destroy
+    if (can_be_destroyed?)
+      super
+    end
+  end
+
+  def can_be_destroyed?
+    !exercises.any?
+  end
+
+  def to_s
+    name
+  end
+
+end

app/models/user_exercise_feedback.rb

@@ -0,0 +1,11 @@
+class UserExerciseFeedback < ActiveRecord::Base
+  include Creation
+
+  belongs_to :exercise
+
+  validates :user_id, uniqueness: { scope: [:exercise_id, :user_type] }
+
+  def to_s
+    "User Exercise Feedback"
+  end
+end

app/models/user_exercise_intervention.rb

@@ -0,0 +1,11 @@
+class UserExerciseIntervention < ActiveRecord::Base
+
+  belongs_to :user, polymorphic: true
+  belongs_to :intervention
+  belongs_to :exercise
+
+  validates :user, presence: true
+  validates :exercise, presence: true
+  validates :intervention, presence: true
+
+end

app/models/user_proxy_exercise_exercise.rb

@@ -0,0 +1,14 @@
+class UserProxyExerciseExercise < ActiveRecord::Base
+
+  belongs_to :user, polymorphic: true
+  belongs_to :exercise
+  belongs_to :proxy_exercise
+
+  validates :user_id, presence: true
+  validates :user_type, presence: true
+  validates :exercise_id, presence: true
+  validates :proxy_exercise_id, presence: true
+
+  validates :user_id, uniqueness: { scope: [:proxy_exercise_id, :user_type] }
+
+end